Go back to the Preprocessing page. This link might be useful to keep track of the files created during the preprocessing.

Let us set some global options for all code chunks in this document.

knitr::opts_chunk$set(
  message = FALSE,    # Disable messages printed by R code chunks
  warning = FALSE,    # Disable warnings printed by R code chunks
  echo = TRUE,        # Show R code within code chunks in output
  include = TRUE,     # Include both R code and its results in output
  eval = TRUE,       # Evaluate R code chunks
  cache = FALSE,       # Enable caching of R code chunks for faster rendering
  fig.align = "center",
  out.width = "60%",
  fig.dim = c(8,8),
  retina = 2,
  error = TRUE,
  collapse = FALSE
)
rm(list = ls())
set.seed(1982)

1 Import libraries

# Install R-INLA package
# install.packages("INLA",repos = c(getOption("repos"),INLA ="https://inla.r-inla-download.org/R/testing"), dep = TRUE)
# Update R-INLA package
# inla.upgrade(testing = TRUE)
# Install inlabru package
# remotes::install_github("inlabru-org/inlabru", ref = "devel")
# Install rSPDE package
# remotes::install_github("davidbolin/rspde", ref = "devel")
# Install MetricGraph package
# remotes::install_github("davidbolin/metricgraph", ref = "devel")

library(INLA)
library(inlabru)
library(rSPDE)
library(MetricGraph)

library(dplyr)
library(plotly)
library(scales)
library(patchwork)
library(tidyr)
library(ggplot2)
library(sf)

library(here)
library(rmarkdown)
library(grateful) # Cite all loaded packages

rm(list = ls()) # Clear the workspace
set.seed(1982) # Set seed for reproducibility

2 Load the data

# Load the graph-processed data
load(here("data_files/data_day7142128_hour13_with_no_consecutive_zeros_27JUN2024_FRC013456_graph_processed.RData"))
# Load the graph
load(here("data_files/graph_construction_on_27JUN2024_FRC013456.RData"))

3 Prepare the data for modeling

# Define standardize function to standardize the data
standardize <- function(x) {return((x - mean(x)) / sd(x))}

# Remove datetime variable
data_on_graph <- data_on_graph %>% 
  dplyr::select(-datetime)

# Perform a more exhaustive filtering
# Create a dataset with speed observations equal to zero and distance to the graph greater than 0.001
to_remove <- data_on_graph %>% 
  filter(speed == 0, .distance_to_graph > 0.001) 

# Filter the data
data_on_graph <- setdiff(data_on_graph, to_remove) %>% # Remove observations with speed equal to zero and distance to the graph greater than 0.001
  filter(.distance_to_graph <= 0.003) # Remove observations with distance to the graph greater than 0.003

# Add the observations to the graph
sf_graph$add_observations(data = data_on_graph, 
                          group = "day", 
                          normalized = TRUE, 
                          clear_obs = TRUE)

# Get the value of the weights (covariates) on the locations of the speed observations
sf_graph$edgeweight_to_data(data_loc = TRUE)

# Create a dataset data with the speed and (standardized) SpeedLimit variables
data <- sf_graph$get_data() %>% # get the data from the graph
  drop_na(-StreetName) %>% # Drop all rows with at least one NA value but without taking into account StreetName (which has NAs). This is because sf_graph$edgeweight_to_data(data_loc = TRUE) creates NAs but we don't want to remove the rows with NAs in StreetName (because those are original NAs in the dataset).
  mutate(across(c("SpeedLimit"), ~standardize(.))) %>% # Standardize the SpeedLimit variable
  dplyr::select(speed, SpeedLimit) # Select only the speed and SpeedLimit variables

# Add the observations to the graph (now with the values of the covariate)
sf_graph$add_observations(data = data, 
                          group = "day", 
                          normalized = TRUE, 
                          clear_obs = TRUE)

# Define a data frame to create the indexingroup variable, which is used to compute the groups
points = data %>%
  as.data.frame() %>%
  mutate(., index = 1:nrow(.)) %>% 
  dplyr:::select(speed, .group, index) %>%
  mutate(.group = as.numeric(.group)) %>%
  group_by(.group) %>%
  mutate(indexingroup = seq_len(n())) %>%
  ungroup()

4 Compute the distance matrices and the groups for cross-validation

# Create an auxiliary dataset aux with the edge_number, distance_on_edge, and group variables to compute the distance matrix
aux <- data |>
  rename(distance_on_edge = .distance_on_edge, edge_number = .edge_number) |> # Rename the variables (because sf_graph$compute_geodist_PtE() requires so)
  as.data.frame() |> # Transform to a data frame (i.e., remove the metric_graph class)
  dplyr::select(edge_number, distance_on_edge, .group) # Select only the edge_number, distance_on_edge, and group variables

# Initialize the list distmatrixlist to store the distance matrices
distmatrixlist <- list()

# Compute the distance matrices for each group
for (i in 1:4) {
  distmatrixlist[[i]] <- sf_graph$compute_geodist_PtE(PtE = aux %>% 
                                                       filter(.group == as.character(i)) %>% 
                                                       dplyr::select(-.group),
                                                     normalized = TRUE,
                                                     include_vertices = FALSE)
}

# Define the distance vector (200m)
distance = seq(from = 0, to = 200, by = 20)/1000

# Compute the groups for cross-validation
GROUPS <- list()
for (j in 1:length(distance)) {
  print(j)
  GROUPS[[j]] = list()
  for (i in 1:nrow(points)) {
    rowi <- points[i, ]
    which.in.group <- which(as.vector(distmatrixlist[[rowi$.group]][rowi$indexingroup,]) <= distance[j])
    GROUPS[[j]][[i]] <- filter(points, .group == rowi$.group)[which.in.group, ]$index
  }
}

# Save the groups
save(GROUPS, file = here("data_files/GROUPS.RData"))

4.1 Check the groups

point_of_interest <- 56011 # Any number between 1 and nrow(data) = 56011
distance_around <- 11 # Any number between 1 and length(distance) = 11

# Get the group of the point of interest
# This determines the next plots
data[point_of_interest, ]$.group 
## [1] "4"
# Get the neighborhood of the point of interest
neighborhood <- GROUPS[[distance_around]][[point_of_interest]]

# Data frame with the neighborhood
windowofinterest <- data[neighborhood, ] |> as.data.frame() |> st_as_sf(coords = c(".coord_x", ".coord_y"), crs = 4326)

# Get the bounding box of the neighborhood
bbox <- st_bbox(windowofinterest)

# Construct the polygon of the bounding box, which will be used to filter the data
polygon <- st_polygon(list(rbind(
  c(bbox["xmin"], bbox["ymin"]),
  c(bbox["xmax"], bbox["ymin"]),
  c(bbox["xmax"], bbox["ymax"]),
  c(bbox["xmin"], bbox["ymax"]),
  c(bbox["xmin"], bbox["ymin"])
))) |>
  st_sfc(crs = st_crs(windowofinterest))

# Filter the data, keeping only the points in the bounding box
data_final_filtered <- data %>% 
  as.data.frame() %>%
  st_as_sf(coords = c(".coord_x", ".coord_y"), crs = 4326) %>%
  st_filter(x = ., y = polygon, .predicate = st_within)

4.1.1 Plot the data

In black, all the points that belong to the group (or replicate) of the point of interest. In blue, the points in the neighborhood of the point of interest. In red, the point of interest.

# Plot the data 
# in black, all the points that belong to the group (or replicate) of the point of interest
# in blue, the points in the neighborhood of the point of interest
# in red, the point of interest
(ggplot() +
  geom_sf(data = polygon, fill = "green", color = "green", alpha = 0.5) +
  geom_point(data = filter(data, .group == data[point_of_interest, ]$.group), aes(x = .coord_x, y = .coord_y), color = "black") +
  geom_point(data = data[neighborhood, ], aes(x = .coord_x, y = .coord_y), color = "blue") +
  geom_point(data = data[point_of_interest, ], aes(x = .coord_x, y = .coord_y), color = "red") +
  ggtitle("Point of interest and its neighborhood") + 
  theme_minimal() + 
  theme(text = element_text(family = "Palatino"))) %>% ggplotly()

4.1.2 Plot all the data in all groups that fall within the bounding box of the neighborhood

Color indicates the group (or replicate).

# Plot all the data in all groups that fall within the bounding box of the neighborhood
# Color indicates the group (or replicate)
ggplot() +
  geom_sf(data = data_final_filtered, aes(color = .group)) +
  ggtitle("All points within the bounding box of the neighborhood") + 
  theme_minimal() + 
  theme(text = element_text(family = "Palatino"))

4.1.3 Plot all the data in all groups that fall within the bounding box of the neighborhood plus the point of interest and its neighborhood

Color indicates the group (or replicate). In red, the point of interest. In blue, the points in the neighborhood of the point of interest.

# Plot all the data in all groups that fall within the bounding box of the neighborhood + the point of interest and its neighborhood
# Color indicates the group (or replicate) of the point
# in red, the point of interest
# in blue, the points in the neighborhood of the point of interest
ggplot() +
  geom_sf(data = data_final_filtered, aes(color = .group)) +
  geom_point(data = data[neighborhood, ], aes(x = .coord_x, y = .coord_y), color = "blue") +
  geom_point(data = data[point_of_interest, ], aes(x = .coord_x, y = .coord_y), color = "red") +
  ggtitle("Point of interest and its neighborhood") + 
  theme_minimal() + 
  theme(text = element_text(family = "Palatino"))

4.1.4 Plot of the point of interest and its neighborhood

In red, the point of interest. In blue, the points in the neighborhood of the point of interest.

# Plot of the point of interest and its neighborhood
# in red, the point of interest
# in blue, the points in the neighborhood of the point of interest
ggplot() +
  geom_point(data = data[neighborhood, ], aes(x = .coord_x, y = .coord_y), color = "blue") +
  geom_point(data = data[point_of_interest, ], aes(x = .coord_x, y = .coord_y), color = "red") +
  ggtitle("Point of interest and its neighborhood") + 
  theme_minimal() + 
  theme(text = element_text(family = "Palatino"))

5 Get the covariate on the mesh

# Define the mesh size
h <- 0.05

# Build the mesh
sf_graph$build_mesh(h = h)

# Get the value of the covariate on the mesh
mesh <- sf_graph$edgeweight_to_data(mesh = TRUE, 
                                   add = FALSE, 
                                   return = TRUE) %>% 
  filter(.group == 1) %>% # Filter by group 1 (or any other group). This is because 4 copies are created, but we only need one
  mutate(across(c("SpeedLimit"), ~standardize(.))) %>% # Standardize the SpeedLimit variable
  dplyr:::select.data.frame(SpeedLimit) # Select only the SpeedLimit variable

# Save all the variables and objects
save(sf_graph, data, points, mesh, file = here("data_files/before_modeling.RData"))

6 References

cite_packages(output = "paragraph", out.dir = ".")

We used R version 4.4.0 (R Core Team 2024) and the following R packages: here v. 1.0.1 (Müller 2020), htmltools v. 0.5.8.1 (Cheng et al. 2024), INLA v. 24.6.27 (Rue, Martino, and Chopin 2009; Lindgren, Rue, and Lindström 2011; Martins et al. 2013; Lindgren and Rue 2015; De Coninck et al. 2016; Rue et al. 2017; Verbosio et al. 2017; Bakka et al. 2018; Kourounis, Fuchs, and Schenk 2018), inlabru v. 2.10.1.9010 (Yuan et al. 2017; Bachl et al. 2019), knitr v. 1.47 (Xie 2014, 2015, 2024), listviewer v. 4.0.0 (de Jong, Gainer, and Russell 2023), mapview v. 2.11.2 (Appelhans et al. 2023), MetricGraph v. 1.3.0.9000 (Bolin, Simas, and Wallin 2023b, 2023a, 2023c, 2024; Bolin et al. 2023), patchwork v. 1.2.0 (Pedersen 2024), plotly v. 4.10.4 (Sievert 2020), rmarkdown v. 2.27 (Xie, Allaire, and Grolemund 2018; Xie, Dervieux, and Riederer 2020; Allaire et al. 2024), rSPDE v. 2.3.3.9000 (Bolin and Kirchner 2020; Bolin and Simas 2023; Bolin, Simas, and Xiong 2023), scales v. 1.3.0 (Wickham, Pedersen, and Seidel 2023), sf v. 1.0.16 (Pebesma 2018; Pebesma and Bivand 2023), tidyverse v. 2.0.0 (Wickham et al. 2019), TSstudio v. 0.1.7 (Krispin 2023), xaringanExtra v. 0.8.0 (Aden-Buie and Warkentin 2024).

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